Process control hardware and software is a major component of almost all installations of chemical, pharmaceutical and refining industries, and is a multi-billion dollar business worldwide. Although obtaining the best possible control in any particular instance has not always been a major focus in the past, in recent years, new plants, such as industrial process plants, are increasingly being designed with controllability and optimizability in mind. Moreover, many existing process plants are being renovated with this objective. This renovation includes not only the renovation of the geometry of the installed hardware, such as the locations of reactors, tanks, pipes, etc., but also renovation of the locations of and types of control, monitoring and measurement elements used to perform process control. With the increasing cost of natural resources and the effective costs associated with emissions, energy consumption has also become a significant factor in plant design.
Control performance monitoring, in combination with controller retuning or model scheduling, can dramatically improve the efficiency of industrial plants and thereby save millions of dollars annually. Another technique that has become increasingly popular in the recent years is abnormal situation monitoring and prevention (ASP). In some cases, modern device and control system designs include novel sensors and embedded statistical algorithms that are able to predict potential failures or upcoming maintenance cycles. These predictive maintenance systems can dramatically increase the uptime of plant operations and prevent costly and dangerous manifestations of unexpected shutdowns. Moreover, the reliability of these techniques has significantly increased in the last decade, leading to increased plant efficiencies.
As part of these efforts, a class of predictive control techniques, generally referred to as model predictive control (MPC) techniques, has gained significant acceptance in the industry since first being developed and applied about 25 years ago. Generally speaking, MPC refers to a class of control algorithms that compute a manipulated variable profile by utilizing a process model (which is typically linear in nature) to optimize a linear or quadratic open-loop performance objective, subject to constraints, over a future time horizon. The first move of this open loop, optimal manipulated variable profile is then implemented within the process, and the procedure is repeated at each control interval or controller cycle to perform process control. Process measurements are used to update the optimization problem during ongoing control. This class of control algorithms is also referred to as receding horizon control or moving horizon control.
However, due to its complexity, MPC has established its place mainly in the advanced control community, and thus MPC configurations are typically developed and commissioned by control experts. As a result, MPC implementations have usually only been worthwhile to apply on processes that promise large profit increases in return for the large cost of implementation. Here, the scale of MPC applications in terms of the number of inputs and outputs has usually been large, which is one reason why MPC has not typically been used in low-level, loop control such as single variable loop control.
More specifically, the commissioning costs of a control system are substantial, and it is rarely practical to pay detailed attention to the configuration of every control loop in a particular process plant. As a result, about 90 percent of all control loops are controlled by traditional linear feedback controllers, such as proportional-integral-derivative (PID) controllers or proportional-integral (PI) controllers. Moreover, to the extent that MPC controllers are used, these controllers are also typically linear in nature. Unfortunately, while linear controllers are predominantly used in the process control industry, the majority of real processes exhibit nonlinear behavior. The consequence of this discrepancy is that model mismatch is unavoidable. Unaddressed model mismatch not only results in suboptimal control performance, but also nullifies many of the advantages of the technologies that have been developed to improve control performance and uptime. Model mismatch is therefore not only costly in terms of the control hardware and software, but actually diminishes the cost savings of other related plant technologies.
Generally speaking, the performance of industrial controllers can be measured in various ways, and different processes may have greatly different quality and safety requirements. Plant engineers may in fact use one or many different performance criteria, such as overshoot, arrest time (integrating processes), oscillation characteristics, integrated error and integrated absolute error (IAE) to evaluate the performance of a particular control loop. However, for PID controllers, the measured control performance for a given controller is typically a result of a tradeoff between set point tracking and disturbance rejection behavior, with better performance in set point tracking resulting in worse performance in disturbance rejection, and vice versa. For example, long time constants (i.e., such as those present in lag dominant processes) are known to cause poor disturbance rejection performance in PID controllers that are tuned for set point tracking performance. This tradeoff, which is inherent in the development of PID controllers, can be explained by the fact that a PID controller that is ideally tuned for load disturbance rejection must have a relatively high integral action (i.e., a relatively small integral time constant), and that high integral action is detrimental to the set point change performance of the controller. More particularly, during a set point change, the process error (e) remains large for a period of time even while the controlled variable (y) is approaching the set point (SP). With very large integral gain, the integral term builds up fast, and more than necessary, thus causing set point overshoot. Consequently, PID tuning targeted for set point change performance has smaller integral action and worse load change or disturbance rejection performance. Because traditional PID control, which as noted above, is still the most popular controller choice in all industries, suffers this problem, many approaches have been suggested in an attempt to reduce the effects of this issue, including structural modifications to the PID controller and set point filtering.
However, even with these modifications, tuning of PID controllers still presents the challenge of correctly specifying the tradeoff between set point tracking and disturbance rejection performance. Different PID tuning methods typically favor one of set point tracking performance or disturbance rejection performance over the other. Moreover, many model based tuning techniques match the internal parameters of a PID controller to internal parameters of a model for the process being controlled, resulting in this same tradeoff. For example, PID tuning methods, such as pole cancellation and lambda tuning, match the integral time of the controller to the dominant time constant of the process. Here, the controller gain is set to achieve a certain closed loop time constant and a certain set point change response (e.g. no overshoot). Because the resulting integral action of such controllers is relatively small, this technique exhibits very good set point change performance, but poor disturbance rejection performance. On the other hand, empirical PID tuning methods such as Ziegler-Nichols methods are specifically designed for disturbance rejection performance. However, because the integral action of such controllers is strong enough to return the process variable to the set point very quickly, it leads to undesired set point overshoot in response to set point changes.
In rare occasions, the purpose of a loop is only disturbance rejection (e.g., a buffer tank level with no set point changes) or only set point tracking (e.g., a secondary loop in a cascade strategy with no disturbances). While in those cases it may be easy to choose a tuning configuration, the aforementioned tradeoff is frequently overlooked entirely and, instead, a default tuning method is typically chosen, making the tuning less than optimal in any particular process situation. As noted above, while numerous tuning methods have been developed to overcome this limitation of PID tuning, including set point filtering and two degree of freedom structures, these tuning methods typically favor disturbance rejection performance, and thus the controller reaction to set point changes is artificially reduced. For example, if set point filtering is chosen, set point changes by the operator are filtered to prevent overshoot, resulting in slower reaction to set point changes.
In any event, a direct outcome of the performance tradeoff discussed above is that different tuning methods have to be chosen for different control objectives, which is one of the reasons why so many tuning methods have been proposed for PID tuning. Another reason for the availability of so many PID tuning techniques is that different tuning rules or methods use different input variables, only some of which may be readily available in any particular process. For example, while many tuning methods calculate tuning based on a process model, other methods calculate tuning based on other process characteristics. As an example of this later method, Ziegler-Nichols tuning rules use critical gain and critical frequency, which may be easy to determine for some mechanical processes, but cannot be practically determined in many industrial chemical processes.
On the other hand, a predictive controller such as an MPC controller should be able to perform similarly for set point changes and load changes because the integral part of an MPC controller does not suffer the same tradeoff as observed for PID controllers. More particularly, MPC controllers generally do not exhibit a performance tradeoff between set point tracking and disturbance rejection because the terms for the error and move penalties are inherently separate, theoretically making MPC controllers a desirable substitute to PID controllers. Also, in a predictive controller, the error (e) does not increase while the controlled variable or process output (y) is approaching the set point. In fact, the error can theoretically be zero after the first execution cycle, thereby decreasing or eliminating the integral gain problems inherent in PID control. Unfortunately, performance of an MPC controller can fall off rapidly when process model mismatch is present, i.e., when the process model being used by the MPC controller does not perfectly match the actual process characteristics.
Still further, it is known that the disturbance rejection performance of industrial MPC controllers lags behind that of PID controllers when PID controllers are specifically tuned for disturbance rejection. Recent MPC improvements in the area of state update have closed this performance gap somewhat if an observer model used in the MPC technique is assumed to be known perfectly. However, in the presence of model mismatch, the control performance of a PID controller, as measured by the integrated absolute error (IAE), is still better than that of an MPC controller with the best possible tuning.
None-the-less, MPC has been considered as one of the prime control technologies to be used in replacing PID controllers as MPC controllers are believed to be able to combine the benefits of predictive control performance and the convenience of only a few more or less intuitive tuning parameters. However, at the present time, MPC controllers generally have only succeeded in industrial environments where PID control performs poorly or is too difficult to implement or maintain, despite the fact that academia and control system vendors have made significant efforts in recent years to broaden the range of MPC applications. Basically, because PID control still performs better than MPC for a significant number of processes, and because PID controllers are cheaper and faster to deploy than MPC type controllers, MPC controllers have actually replaced only a small fraction of PID controllers within actual process plant configurations.
One of the main reasons why MPC controllers tend to perform worse than PID controllers is that, as indicated above, MPC controllers are more susceptible to performance degradation as a result of process model mismatch than PID controllers (except possibly in lag dominant processes). While there are practical ways to address the model mismatch that results from nonlinearities (or other sources) in processes, such as the linearization of the control elements and the transmitters and the use of controller gain scheduling, the most common technique to address model mismatch is to implement controller tuning. Because of the difficulties in tuning controllers, however, process operators or engineers frequently tune a controller for the worst case scenario (e.g. the highest process gain) and accept suboptimal tuning for other regions of the process. The default tuning parameters of an industrial PID or MPC controller are thus typically conservative, so that these tuning parameters can work initially for a variety of process applications. However, controllers are usually left at their default settings indefinitely, resulting in overall poorer performance. Even if this were not the case, the model mismatch that results from identification error or from plant drift is more difficult to address with tuning. In fact, this type of model mismatch is hard to detect because sufficient process perturbation is required to implement model identification, which typically contradicts the objective of process control (i.e., keeping the process at steady state in response to process disturbances). Moreover, it is hard to distinguish process perturbation from unmeasured disturbances.
One method of “tuning” an MPC controller in response to model mismatch is to regenerate the process model in light of process changes and then use this new model within the MPC controller. Unfortunately, there are many practical obstacles to developing an accurate process model for use in model based controllers in the first place. For example, even though many industrial processes are minimum phase, the majority of closed loops are not minimum phase. Time delay, also known as deadtime, and higher order lags create right hand poles which greatly complicates the development of an accurate process model. In most instances, closed loop deadtime is created by transport delay of material in pipes and discrete sampling mechanisms that are unavoidable in computer control systems, while higher order lags are usually a result of filter time constants in measuring and control devices. Other challenges often found in defining process models for industrial plants include resolution and deadband created by the mechanical behavior of valves and packing.
These and other factors present many challenges to control engineers in industrial plants when developing process models for controllers. For example, even if a certain process is expected to act like a first order filter with certain gain and time constant, depending on vessel geometry, the control engineer has to consider additional time constants from transmitters, control elements computer sampling and jitter. In particular, any digital control system has central processing unit (CPU) and communication constraints, which means that ample over-sampling is not practical for all types of loops in a plant. For example, while a sampling rate of three times the largest time constant plus deadtime or five times the deadtime, whichever is larger, is often considered reasonably sufficient, this sampling rate is usually not achievable for many control loops in a plant (such as flow loops and pressure loops). As a result, the engineer can not usually rely solely on the first principle models that may be available for some of the reactions. Moreover, process model identification is ideally performed by integrated automatic tools. However, the first principle modeling and universal third party solutions that are typically used in a real plant to identify a process model do no by connecting directly to the field instruments. These solutions are not therefore integrated because they do not consider (or at best only approximate) the effect of the computer control system itself on loop performance. All of these factors can result in significant mismatch between the process and the process model developed to control the process, making model-based control and tuning methods less desirable in practical situations.
One very important and promising type of MPC controller is that which uses a state update technique or an observer model. There is abundant literature on state update methods used in MPC, and many techniques have been developed that improve the performance of the state update component of a model predictive controller to provide a very responsive MPC controller. However, because model based controller performance can be severely degraded by model mismatch, the majority of efforts to improve control performance in model predictive controllers is focused on improving the performance and precision of state update algorithms that correct for the effects of model mismatch. Another large portion of control literature is concerned with improving initial model quality, adapting process models to process parameter changes, or detecting process parameter changes in order to inform the user and trigger a manual process model reevaluation. Unfortunately, these techniques are not practical in many instances, and few of them make the MPC controller perform comparable to or better than PID controllers in a wide variety of instances.